I also have a game that fits that description! I'm planning to self-publish mine, starting with a PDF on DriveThruRPG and maybe going print-on-demand if there's... well, 'demand'.
Kickstarter can be handy if you need funds for art, layout, editing and such, to make it look professional. However, I hear it's a pretty intense process, and you need to do a lot of prep to make sure the numbers are right. Since I have art and layout skills myself, I'm just slowly producing my game 'in-house' and will release it when it's ready.
I don't know much about game or publishing companies to approach about an original RPG. Physical copies seem to be the hard part, since you basically have the option of small-run traditional printing (500+ copies probably), or print-on-demand through DTRPG, Lulu, or somewhere like that. Also as I'm in Australia, dealing with shipping to/from the US is kind of annoying and cost-prohibitive. PDF is a really good entry option for me, and I'll be providing a tricked-out file to make the document as easy to use as possible.
I do freelance editing, layout, and artwork, but I would need to charge – I'm working on too many of my own projects to donate my time sorry! :)